Question

A $10mg$ effervescent tablet containing sodium bicarbonate and oxalic acid releases $0.25ml$ of $C{O}_2$ at $T=298.15K$ and $p=1bar$. If molar volume of $C{O}_2$ is $25.9L$ under such conditions, what is the percentage of sodium carbonate in each tablet?
(Molar mass of $NaHC{O}_3$ is $84g/mol$)
A.$16.8$
B.$8.4$
C.$0.84$
D.$33.6$

Answer 1

Hint: To calculate the percentage of sodium carbonate in the tablet first calculate the relation between the number of moles of sodium carbonate and number of moles of carbon dioxide then apply the mole concept.

Complete step by step answer:
First we will talk about how to calculate the number of moles.
Number of moles: Number of moles can be defined as the ratio of given mass to the molar mass of the substance. Or we can find the number of moles of a substance by the ratio of given volume to the molar volume.
In the question it is given that the molar volume of carbon dioxide is $25.9L$ and the volume of carbon dioxide produced is $0.25ml$. So number of moles $={\displaystyle \frac{\text{given volume}}{molar\text{ volume}}}$
$$n={\displaystyle \frac{0.25\times {10}^{-3}}{25.9}}\approx {10}^{-5}$$
The reaction of sodium bicarbonate with oxalic acid is as
$2NaHC{O}_3+H_2{C}_2{O}_4\to 2Na{C}_2{O}_4+2H_{2}O+2C{O}_2$
By the reaction, it is clear that two moles of sodium bicarbonate are forming two moles of carbon dioxide. Hence one mole of sodium bicarbonate will form one mole of carbon dioxide.
We already calculated the number of moles of carbon dioxide i.e. ${10}^{-5}$.
And the number of moles of sodium bicarbonate and number of moles of carbon dioxide are the same. So the number of moles of sodium bicarbonate will be ${10}^{-5}$. Now the molar mass of sodium bicarbonate is $84g/mol$.
So the mass of sodium bicarbonate present will be as molar mass multiply number of moles i.e. $84\times {10}^{-5}g$
Now, the percentage of mass i.e. $\mathrm{\%}$mass $={\displaystyle \frac{84\times {10}^{-5}}{10\times {10}^{-3}}}\times 100=8.4\mathrm{\%}$.
Hence, the correct answer is option B.

Note:
 If we want to calculate a given mass and if we have a number of moles and molar mass of the substance then we can calculate the required mass as: number of moles multiply by molar mass of the substance.